Blue was recognized as a past Champion and at the time considering Giovanni came out of hiding, Blue most likely retired as Gym Leader (a job he didn't really like from what I remember in HG/SS) and was replaced again by Giovanni who Blue was only taking the spot of.
Blue and Red are both recognized as Champions so they were invited along with Alder, Cynthia, Steven, and Wallace. Steven and Wallace both being in the same bracket presents a worse scenario than lack of Koga as it acknowledges two separate dimensions of storyline UNLESS you go with past Champions being allowed to compete.
Iris isn't in the current roster because the B2W2 PC replaces her as Champion (second time as far as I remember that a PC is thoroughly recognized as a Champion in game, first being Red in G/S).
Based on this timeline speculation, Blue a retired Gym Leader AND Old Champion was invited as a Champion to take place with Giovanni sporting the Gym Leader role. Leaving the current Champion Lance to be a representative for Johto. Koga, being an Elite Four member stayed behind to protect Johto and his Daughter who succeeded him as Gym Leader went to compete.
Giovanni, Lace, Blue, Red, Wallace, Steven, and Juan are the only real conflicting bodies in the tournament, but its easy to summarize a reason why they are there. All currently recognized Elite Four members stayed behind "to protect their regions while the Champion is away".